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Statistics (the science)

  • a mathmatical science pertaining to the collection, analysis, interpretation, explanation, and presentation of data; A set of mathematical procedures for organizing, summarizing, and interpreting information.  

Statistic (singular)

  • A value, usually a numerical value, that describes a sample. Usually derived from measurements of the individuals in a sample.




Descriptive Statistics vs. Inferential Statistics

  • Descriptive: Statistical procedures used to summarize, organize, and simplify data.



  • Inferrential: Consists of techniques that allow us to study samples and then make generalizations about the populations from which they were selected; generalize findings from a sample group to the larger population



Correlational Method vs. Experimental Method

  • Correlational: Two different variables are observed (not manipulated) to determine whether there is a relationship between them.



  • Experimental: One variable is manipulated (independent); another variable is observed and measured. (dependent) to establish a cause-and-effect relationship between the two variables, an experiment attempts to control all other variables to prevent them from influencing the results.


 

Experimental Group vs. Control Group

  • Experimental: receives the experimental treatment.



  • Control: does not receive the experimental treatment or receives a neutral, placebo treatment instead; Provides a baseliine for comparison with the expirimental condition.

Sample

  • A set of individuals selected from a population intended to represent the population



Data (plural) vs. Datum/score/raw score (singular)
vs. Information

  • Data: the measurements (numbers, scores, and so forth) collected in a research study before they have been analyzed in any way.



  • Datum/Score/Raw Score: A SINGLE measurement or observation collected



  • Information: interpretation given to collected data after they have been analyzed.  p.04

Data Set

  • A collection of measurements or observations.



Variables vs. Constants

  • Variables: characteristics or attributes that DIFFER in quantity or quality among the people (or objects) studied; are operationalized are tested by hypothesis  p. 04



  • Constants: traits or characteristicts that DO NOT differ in quantity or quality among the people (or objects) studied. p. 04

Values vs. Value Categories

  • Values: different measurments of a variable expressed in numbers QUANTITATIVE form that reflect differences in the quantity of the variable and reflect more precise measurment than value categories. p. 05



  • Value Categories: different forms the variable can take; QUALITATIVE data; DISCRETE; NOMINAL level  p. 05

Frequency

  • number of times a value category or value occurs within a group of cases. p. 05

Conceptualization vs. Operationalization

  • Conceptualization: the process of selecting what variable(s) need to be measured. p. 06



  • Operationalization: specifying exactly HOW variable(s) which have been conceptualized are going to be measured p. 06

Reliability vs. Validity
Reliability: the degree of consistency of a measurement p. 07

Validity: when measurement is both reliable (consistent) AND truly measuring what it is believed to be measuring.  p. 07
Research Hypotheses
a statement that we make about what we believe to be the relationship between or among variables. p. 08
one-tailed hypothesis vs. two-tailed hypothesis vs. null hypothesis
  • One-Tailed: goes further than a two-tailed hypothesis and predicts not only a relationship, (whether correlation or association), but the DIRECTION of the relationship, as in possible cause and effect; indicating a causal relationship (p. 10)
  • Two-Tailed: Predicts which variable will be associated with another variable; predicts only a relationship between specific variables, such as a correlation or an association; indicating a non-casual relationship (p.10)
  • Null: predicts two or more variables are NOT RELATED

most frequently used type of research hypothesis by social workers

  • CAUSUAL research hypothesis; one-tailed

Positive Correlation vs. Negative Correlation

  • Positive: high values of one variable found with high values of the other variable



  • Negative: high values of one variable found with low values of the other variable p. 10

Independent Variable vs. Dependent Variable

  • Independent: the variable that is manipulated by the researcher and predicted to influence the dependent variable  p. 11



  • Dependent: The variable whose variations we are seeking to understand and that is believed to be influenced by the independent variable; a variable which is impacted by other variables..  p. 11

Variable Levels of measurement (4)

    • nominal

    • ordinal

    • interval

    • ratio

(1) Nominal Level variable Measurement

  • least precise level of measurment.  Its values are discrete, which means that they are distinct from each other and categorized into discrete subclasses; have two or more value labels. The different value categories it uses reflect only a difference in kind (qualitative data) and do not make any quantitative distinctions between observations.

(2) Ordinal Level variable Measurement

  • Consists of a set of value categories that are rank-ordered (organized in an ordered sequence) in terms of size or magnitude, ranging from high to low or from most to least. p. 14

(3) Interval Level variable Measurement

  • Like ordinal level measurement, interval level meaurement consists of rank-ordered categories, but unlike ordinal level measurement it places the values for the variable on an equally spaced continuum; a uniform unit of measurement in which all intervals are exactly the same size. Equal differences between numbers on scale reflect equal differences in magnitude. However, the zero point on the interval level is arbitrary and does not indicate a zero amount of the variable being measured. (no absolute zero point) p. 15 

(4) Ratio Level variable Measurement

  • Identical to Interval Level Measurement EXCEPT that it has a fixed, absolute, and nonarbitrary zero point. p. 15

Categorical/Discrete Variables vs. Continuous Variables

  • Categorical/Discrete: also known as qualitative variables. Categorical variables can be further categorized as either nominal, ordinal or dichotomous; takes on only a finite number of values, consisting of separate, indivisible categories. No values can exist between two neighboring categories. p. 17



  • Continuous: takes on an infinite number of possible values and is divisible into an infinite number of fractional parts. p. 17  Continuous variables are also known as quantitative variables; numerical. Continuous variables can be further categorized as either interval or ratio variables.

Dichotomous variable

  • nominal variables which have only TWO categories or levels

Population

  • The set of all the individuals of interest in a particular study.

Parameter

  • A value, usually a numerical value, that describes a population. Usually derived from measurements of the individuals in a population.



CHAPTER 02 - Frequency Distributions and Graphs
Frequency Distribution

  • An organized tabulation of the number of individuals located in each catagory on the scale of measurement

Percentile vs. Percentile Rank
Percentile: a point below which a certain percentage of the distribution of values lies. each z score corresponds to both a certain z score and a certain percentile rank

Percentile Rank: tells us approximately what percentage of scores falls above or below the raw score
Bar Graph
A graph showing a bar above each score or interval so that the height of the bar corresponds to the frequency. A space is left between adjacent bars.
Line Graph
Points connected with straight lines to form a graph
Ch 3, pg 79
Histogram
A graph showing a bar above each scoreor interval so that the height of the bar corresponds to the frequency and width extends to the real limits.
Polygon
A fraph consisting of a line that connects a series of dots. A dot is placed above each score or intervalso that the height of the dot corresponds to the frequency.
CHAPTER 03 - Measures of Central Tendency and Variability
Central Tendancy
A statistical measurement to determinea single score that defines the center of a distribution - a single score that is most represetitive of the group.
Mode
The score or category in a frequency distrbution that has the greatest frequency
Ch 3, pg 73
Bimodal
A distribution with two modes (catagories that has the greatest frequency)
Ch 3, pg 74
Multimodal
A distribution with more than two sets of modes (catagories that have the greatest frequency)
Ch 3, pg 74
Median
If a distribution is listed from smallest to largest, median is the midpoint of the list.
Mean
The sum of scores in a distribution, divided by the number of scores.
Measures of Variability (5)

  • range

  • interquartile range

  • mean deviation

  • variance

  • standard deviation

Range
the distance that encompasses all values within a data set; (maximum value - minimum value + 1)
why do we add 1 to the difference between the maximum value and the minimum value when determining range?
so that the range reflect the total number of vales of the variable that it encompasses
mean deviation
the average amount that the values of a variable differ (or deviate) from the mean; describes only the amount of variation among values of a variable, not their absolute values
how to configure a deviation value
subtract raw scores from the mean
mean deviation formula
mean deviation = sum of deviation values (ignoring sign)/number of cases
variance formula
variance = the sum of the square of each deviation value/total number of values minus one (for sample data) or simply the total number of values (for population data)
how to configure the variance
subtract the mean of the distribution from each value (getting the mean deviation) then square each difference. Divide the sum of the squared differences (called the sum of squares) by either the total numbr of values minus one (for sample data) or simply the total number of values (for population data)
standard deviation
the square root of the varience; used for describing the variability of a data set; requires interval level or ratio level data and a normal distribution; reflects variation, and the amount of variation does not change
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